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A wire of length L is hanging from a fixed support. The length changes to L₁ and L₂ when masses 1 kg and 2 kg are suspended respectively from its free end. Then the value of L is equal to

Asked in JEE Main 29th June 2nd Shift 2022 · Elongation under a load

• (1) √L₁L₂
• (2) (L₁+L₂)/2
• (3) 2L₁-L₂
• (4) 3L₁-2L₂

Step-by-step solution

Why the other options are wrong

• (1) comes from the geometric mean lies between L₁ and L₂, so it is longer than the unloaded wire; extension is linear in the load, and nothing here calls for a square root.
• (2) comes from the arithmetic mean is the length under a 1.5 kg load, not the unloaded length; both L₁ and L₂ already include an extension that has to be removed, not averaged.
• (4) comes from stepping back the wrong number of intervals: L₂-L₁ is one 1 kg step, so only one step is subtracted from L₁. Two steps would be the length under a -1 kg load.

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